Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.*;

public class Main {
    public static void main (String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken()),
            h = Integer.parseInt(st.nextToken());
        double A = (double)h/2;
        int a = 1,
            b = -2;
        for (int k=n-1 ; k>0 ; k--) {
            double q = (A - (double)k * A / (double)n);
            double c = 1 - 2*q/(double)h;
            System.out.print((double)h-h*solve(a, b, c) + " ");
        }
    }
    
    public static double solve(int a, int b, double c) {
        double x1 = (-(double)b + Math.sqrt((double)b*(double)b - 4 * (double)a*c))/(2*(double)a);
        double x2 = (-(double)b - Math.sqrt((double)b*(double)b - 4 * (double)a*c))/(2*(double)a);
        //    System.out.println(x1 + " " + x2);
        return (x1<x2?x1:x2);
    }
}